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Structural Dynamics Modeling and Testing of an Air-to-Ground Missile System

Larry Lucas US Army RDECOM Aviation and Missile RDEC AMSRD-AMR-PS-PI Redstone Arsenal, AL 35898 Russ Garner US Army RDECOM Aviation and Missile RDEC AMSRD-AMR-PS-PI Redstone Arsenal, AL 35898 Brock Birdsong US Army RDECOM Aviation and Missile RDEC AMSRD-AMR-PS-PI Redstone Arsenal, AL 35898

ABSTRACT The Platform Integration Function, Aviation and Missile Research, Development, and Engineering Center located at Redstone Arsenal, Alabama developed structural dynamics models and performed experimental modal testing on an Air-To-Ground Missile System. The purpose of this project was to understand the dynamic response of the missile during a helicopter launch. The modeling focus began with rigid body dynamics, but quickly shifted to flexible body dynamics with modal testing and correlation. Modal test fixtures were built for missile and launcher testing. This paper will discuss the test fixtures relating to validating the structural dynamics model. The paper will also present an overview of the analysis, testing, fixture design and finite element model correlation as a result of this project. INTRODUCTION The Platform Integration Function of the Aviation and Missile Research, Development, and Engineering Center initiated an investigation into the dynamic response of a missile to the transients resulting from a missile launch. The investigation involved the development of complex analytical models using a flexible multibody dynamics formulation. The goal of the investigation was to gain a greater understanding of the interaction between the missile and host or launching platform. The missile is fired from a two or four rail launcher that is attached to the helicopter through an ejector rack. The ejector rack attaches to the helicopter through a wing and pylon as on the Apache, Figure 1 or through a universal weapons pylon as on the Kiowa Warrior, Figure 2.

Figure 1, Launcher Mounted on the Apache

Figure 2, Launcher Mounted on the Kiowa Warrior The complexity and nature of the weapon system provided both the necessity and the logical subsystems that could be used to develop tests that would help in determining the contributions of each of the subsystems. This led to the need to develop a test fixture that was adaptable to the various different subsystems. The multibody dynamics model was also based on the same subsystems to facilitate validation at the lowest level possible before validating the entire system model. A series of missile flight tests were conducted to provide data for model validation as well as to aid in the basic understanding of this dynamic event. This test series varied firing from a single rail up through the complete wing with pylons and two launchers in the case of the Apache, for a progression in the complexity resulting from adding components. ANALYSIS The multibody dynamics model was developed as a series of submodels including the missile, launcher, pylon, wing for the Apache, and universal weapons pylon for the Kiowa Warrior. The missile to launcher interface was modeled in great detail using contact elements to account for the missile balloting down the launch rail before it separates from the launcher. The release mechanism was also modeled in great detail as this is the source of the load transfer to the launching platform. All launchers must provide a positive retention system to prevent the missile from falling off of the launcher during any maneuvers the helicopter might conduct. This retention is the source of the loading that causes the launching platform to deflect. The amplitude of these deflections is dependent on a rather complex relationship between the impulse applied to the launching platform and the flexibility of the launching platform. The initial dynamics model was developed using rigid multbody dynamics only as an initial step in the development of the model. Upon refining the dynamics model, flexible components were added to characterize the flexible response of the structures. The final model included a flexible wing and pylon for the Apache and flexible pylon arm, ejector rack, and ejector rack mounting plate for the Kiowa Warrior. The flexibility was added to the model using component mode synthesis. In this method, a finite element model (FEM) was developed for each flexible body to predict the constraint and normal modes used to describe the motion of the flexible components applied in the dynamics model. Experimental modal analysis in conjunction with FEM correlation and updating were performed to validate the flexible body models. The results of the FEM correlation and updating are presented in this paper. MISSILE FIRING TESTS The testing associated with the investigation was planned and conducted to collect missile response data and launcher response data during the launch transient event. The tests were conducted in a progression of

increasing complexity based on the submodel development as mentioned in the previous section. A series of approximately 40 channels of data were collected for each missile firing. The data consisted of missile response, and launcher response as measured through strain gages, accelerometers, and rate sensors. FIXTURE DESIGN The fixtures used in the test were designed for firing missiles from numerous configurations for the purpose of collecting test data to correlate the overall dynamics model. The approach was to increase the complexity of the launch stand from a single rail to a full Apache wing or Kiowa Warrior Universal Weapons Pylon (UWP). In the case of the Apache, there were a total of four different test configurations, all requiring test stand reconfigurations, Figures 3-8.

Figure 3, Base Fixture

Figure 4, Fixture with Rail

Figure 5, Fixture with Launcher

Figure 6, Fixture with Pylon and Launcher

Figure 7, Fixture with Wing, Pylons, and Launcher

Figure 8, Fixture with Universal Weapons Pylon These reconfigurations were conducted on site as the testing progressed from simple to complex. The fixture was designed with this in mind and as would be expected the stand was designed with bolted joints. The fixture was designed with the intent of producing a stiff stand, but the schedule did not allow the development of a finite

element model prior to fabrication to verify the stiffness of the stand configurations. Also, funding did not allow for the development of a fixture for each configuration to be tested. FINITE ELEMENT MODELING AND CORRELATION This section discusses finite element modeling and modal test correlation for an Apache helicopter missile launcher test stand and wing. Modal analysis yielded the first 11 modes ranging from 31 to 144 Hz. The first 8 modes were correlated with FEM predictions resulting in Modal Assurance Criteria (MAC) values greater than 87. Finite Element Modeling The challenges of developing the Apache wing and test stand finite element models included adequately representing the boundary conditions and connections of the test stand hardware and wing setup. The FEM and modal test configuration is shown in Figure 9. In general, boundary condition sensitivity relating to frequency and mode shape shifts is ideally identified prior to modal correlation. For the test stand, the boundary conditions where the test stand base plate connects into and contacts the floor greatly affect frequency and mode shape changes in the structure. [1]

Attachment

Stand

Wing

Base Plate

Figure 9, Apache Test Stand and Wing Finite Element Model The challenges of representing the boundary conditions are generally addressed by assumptions in modeling joints like bolted and welded connections, riveted skinned components, and test stand constraints. These joints involve contact, friction, and slip. Often, these components are non-linear elements and sometimes poorly represented by the linear elements in modal analysis. The best representation of the connections and boundary conditions are often derived by engineering judgment and experience. A convergence study of the FEM was performed with a medium and fine mesh to ensure that a modal solution was converged. Results indicate that most of the normal frequencies agree within less than 1 percent of each other. Several areas of uncertainty were identified in the model. The bolted joints between the structural elements, the bolted joints between the test stand and floor, and the contact of the base plate and floor could have the largest modeling errors. A sensitivity study was performed on these areas of uncertainty and it was determined that the bolted joints between the structural elements and the base plate, and the contact of the base plate and floor were

the most sensitive. Changes in the contact boundary conditions, the bolt stiffness, and friction in these bolted joints shifted the frequency and mode shape significantly. Modal Correlation To get a feel for the accuracy of the FEM, a correlation study was performed on the Apache test stand, attachment, and wing model. LMS Gateway® and FEMtools® software were applied for the correlation. The MAC, Correlated Mode Shape Differences (CMD), and Coordinate Modal Assurance Criteria (COMAC) were applied for the Apache test stand and wing model correlation. The MAC analysis compares the deformation vector or mode shape of the correlated node-point pair dofs of the FEM results with the mode shape of the test results. The CMD analysis indicates differences between the mode shape pairs. It is considered a local shape correlation in that "the CMD-values are calculated at the mapped dofs as relative values after scaling of the experimental model shapes. Low CMD-values indicate good correlation, high CMD-value indicate areas with potential modeling errors" [2]. The COMAC analysis shows an indication of correlation between each node and point pair for all the paired mode shapes and is independent of mass and stiffness weighting. "High COMAC-values indicate good correlation over the range of selected modes, low COMAC-values indicate areas with potential modeling errors" [2]. The Apache test stand and wing FEM was correlated and updated. Results are listed and presented in Table 1 and Figure 10. From Table 1, eight modes correlated good with MAC values > 74. Seven of the eight modes correlated well with MAC values > 87. The CMD and COMAC values were examined for a local shape correlation. Both analyses indicated that the tip of the wing had the worst values for correlation. Although this may indicate an area of the model with errors, other discrepancies in the model caused these results. Based on the correlation analysis and examining the mode shape overlay, the cause of these results was due to uncertainty in the bolted connection and contact between the wing and wing attachment. The constraints and boundary conditions in these areas were updated to yield the correlation results in Table 1. Table 1, Apache Test Stand and Wing Correlation and Updating Results FEA Test MAC Mode % (Hz) (Hz) Value 1 35.4 31.4 11.3 96 2 40.3 36.4 9.7 74 3 50.0 44.8 10.4 98 4 57.1 55.0 3.7 87 5 91.7 84.7 7.6 89 6 100.8 86.2 14.5 92 7 115.0 107.8 6.5 91 8 115.3 113.8 1.4 93

MAC

CMD

COMAC

Figure 10, Apache Test Stand and Wing Correlation and Updating Results MODAL TEST AND ANALYSIS The purpose for performing modal tests and analyses on the Apache test stand and wing weapons platform is to provide dynamic information for the correlation of finite element models and dynamic models used in the simulation of missile launch. Specifically the modal test and analysis results will be used to correlate the FEMs representing the Apache test stand and wing weapons platform structure. The modal test and analysis will determine the dynamic characteristics of the Apache test stand and wing platform structure in the form of mode shapes, modal frequencies, and damping. The objective is to perform the modal test and analysis on the Apache test stand and wing platform with boundary conditions as configured during testing at Eglin Air Force Base, Florida. During these tests the test stand and wing was attached to a stationary fixture, as shown in figure 11.

Figure 11, Apache Wing and Test Stand During Modal Testing The test stand is comprised of three primary structures: the test stand, the wing attachment fixture, and the wing. The modal test and analysis was performed on the test stand and on each additional build up of the structure until

the Apache test stand and wing configuration was complete. This allowed each segment of the FEM to be correlated to ensure complete understanding and accuracy of the model results. LESSONS LEARNED To address inadequacies discovered in the Apache test stand and wing correlation, several questions were asked. Is the modal test setup and hardware physically understood? Are the boundary conditions on the test hardware properly represented in the FEM? How much of the wing correlation involved the test stand dynamics? Much time was spent trying to understand the test setup physically and answer questions like these for a successful correlation. The most valuable lesson learned is that from the beginning, the analyst, test fixture designer, and test engineer should plan and develop the project together. The analyst and test engineer should review the proposed test fixture for possible problems or improvements before it is fabricated. For example, the Apache test stand was fabricated independent of the analyst and test engineer's inputs, so that when it was time for testing, there were challenging testing issues with the test stand design. The boundary conditions were difficult to model in the FEM and most of the dynamics of the mode shapes resided in the test fixture instead of the wing. These issues could have been addressed before test stand fabrication. One of the constraints that led to the design of the test fixture base plate could have easily been altered if the relationship between the system dynamic response and modal testing were understood by all involved. Specific to the test fixture design, it is recommended that an FEM analysis on the proposed test fixture be performed prior to fabrication. The FEM analysis can determine if the dynamics of the mode shapes are more pronounced in the test fixture or the test object of interest. It is desirable to have most of the dynamics reside in the test object of interest rather than the test fixture. Connections should be as "rigid" as possible to minimize non-linear compliance in the test fixture. For example, it is better to have welded connections instead of bolted connections if possible. Also, in the case of bolted joints, perhaps a modification as simple as the addition of dowel pins to prevent slipping in the shear plane in conjunction with a sufficient torque requirement could produce joints that can be assembled with some level of repeatability. It is desirable for the boundary conditions of the test fixture to be "fixed" instead of a contact or friction connection. For example, where the test stand base plate contacts the floor, non-linear contact forces developed. To predict these contact forces, it required a more extensive FEM with greater fidelity. From the analyst, it is recommended to develop the FEM robust enough for modal correlation and updating. Develop the model for easy mesh refinement to check convergence. For example, if major changes to the FEM are required just to refine the mesh, more effort should be devoted to modeling. As discussed in this report, element properties, boundary conditions, and material properties should be grouped logically to identify areas of uncertainty and perform sensitivity analyses. It is also desirable to apply the FEM modal predictions to help the test engineer understand the proposed test setup. Another lesson learned is to not assume that the design drawings of the test components perfectly match the hardware. For example, discrepancies between the test stand and missile components and design drawings were discovered. Unfortunately, the discrepancies were discovered after considerable FEM development and therefore were time consuming to correct. From the test engineer, it is recommended that more reliance be placed on the analyst predictions for insight into the mode shapes and frequencies of the test structure. For example, the FEM predictions can give the test engineer understanding of what axis directions to excite so that all the desired modes are measured. Another example, is that when test problems occur, like a bad dof or measurement, the test engineer more readily identifies the problem from the confidence gained through FEM predictions. Lastly, for a successful modal test and correlation, it is recommended that the project be divided into a series of simpler tests and correlations, building confidence and understanding of the test structure as the project progresses. It is proposed for the next modal test and FEM correlation that a series of "free-free" modal tests and FEM correlations be performed on the test fixture and test components before they are integrated and assembled into a final test configuration. This should yield clear understanding of the structures under test.

CONCLUSION In conclusion, it is painfully obvious that fixture design is just as significant as any other step in the modelingtesting-validation process. The mistake of not conducting an analytical modal analysis due to schedule added to the schedule in the end due to the extra time required to correlate and update the stand in the validation phase of the task. Much of this could have been avoided by coordination during the test fixture design phase. Just as important is the overall understanding of the affect of the test fixture on the overall dynamic response of the actual test article. A balance must be created between the ease of testing and the usefulness of the data being collected. REFERENCES 1. Lucas, L. D., Garner, R., Birdsong, B., Apache Launcher Dynamics Prediction with Model Updating and Correlation, Technical Report AMR-PS-04-19, June 2004. 2. Dynamic Design Solutions N.V., FEMtools© Help, Version 2.2, Copyright 1994-2003.

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